Quantifying and Probing Multipartite Entanglement via Minimum Entanglement Drop
Quantifying genuine multipartite entanglement remains a significant challenge. We propose a multipartite entanglement monotone defined by the minimum entanglement drop -- the reduction in global one-to-group entanglement upon tracing out a single particle. We formulate a computationally efficient variant using tangle and negativity to ensure non-vanishing values for W-class states, and rigorously prove it is a valid monotone under local operations and classical communication. In the tripartite regime, the minimum tangle drop is physically equivalent to the minimum pairwise concurrence. We establish an operational framework where the entanglement drop acts as a structural probe: by assessing sensitivity to qubit loss, it identifies inseparable clusters, extracting connectivity fingerprints that uniquely differentiate graph topologies within the same local Clifford equivalence class. Integrating this mapping with classical shadows enables efficient experimental estimation and dynamic tracking of entanglement network evolution. We derive exact analytical solutions for n-qubit W states under environmental noise, revealing robust scaling behaviors. Finally, we acknowledge limitations, noting that diagnostic sensitivity strictly vanishes for highly robust states such as the 5-qubit error-correcting code.